For matrices over Q there's sage.matrix.misc.matrix_rational_echelon_form_multimodular, which is the default for matrices with more than 25 rows/columns. It should be possible to adapt this to number fields.
You might also look into what Pari is capable of, since we're getting our number fields from there and they probably need to do linear algebra with number fields. David On Tue, Apr 7, 2020 at 11:59 AM Vincent Delecroix <20100.delecr...@gmail.com> wrote: > Dear linear algebra specialists, > > I am stuck with an elementary linear algebra problem where > Sage is (for now) of no help. I want to compute the rank of > a 30 x 30 dense matrix over a number field of degree 30. > > sage: x = polygen(QQ, 'x') > sage: K = NumberField(x^30 - 3, 'a') > sage: M = MatrixSpace(K, 30) > sage: m = M.random_element() > sage: m.rank() > > See also > > > https://ask.sagemath.org/question/50626/compute-dimension-of-vector-subspace/ > > Any hint? > > Best > Vincent > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/2f5b1208-e65e-d603-0b73-91121eacb591%40gmail.com > . > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAChs6_%3D0WWa6Y%2BLFQZuc-3Ui2Lh6mEz_yeC3RsEMka%2BQnM3P8Q%40mail.gmail.com.
